Improved resolution in 3D structured illumination microscopy using 3D model-based restoration with positivity-constraint.

The performance of structured illumination microscopy (SIM) systems depends on the computational method used to process the raw data. In this paper, we present a regularized three-dimensional (3D) model-based (MB) restoration method with positivity constraint (PC) for 3D processing of data from 3D-SIM (or 3-beam interference SIM), in which the structured illumination pattern varies laterally and axially. The proposed 3D-MBPC method introduces positivity in the solution through the reconstruction of an auxiliary function using a conjugate-gradient method that minimizes the mean squared error between the data and the 3D imaging model. The 3D-MBPC method provides axial super resolution, which is not the same as improved optical sectioning demonstrated with model-based approaches based on the 2D-SIM (or 2-beam interference SIM) imaging model, for either 2D or 3D processing of a single plane from a 3D-SIM dataset. Results obtained with our 3D-MBPC method show improved 3D resolution over what is achieved by the standard generalized Wiener filter method, the first known method that performs 3D processing of 3D-SIM data. Noisy simulation results quantify the achieved 3D resolution, which is shown to match theoretical predictions. Experimental verification of the 3D-MBPC method with biological data demonstrates successful application to data volumes of different sizes.